The International Arab Journal of Information Technology (IAJIT)


Information Analysis and 2D Point Extrapolation using Method of Hurwitz-Radon Matrices

Information analysis needs suitable methods of curve extrapolation. Proposed method of Hurwitz-Radon Matrices (MHR) can be used in extrapolation and interpolation of curves in the plane. For example quotations from the Stock Exchange, the market prices or rate of a currency form a curve. This paper contains the way of data anticipation and extrapolation via MHR method and decision making: to buy or not, to sell or not. Proposed method is based on a family of Hurwitz-Radon (HR) matrices. The matrices are skew-symmetric and possess columns composed of orthogonal vectors. The operator of Hurwitz-Radon (OHR), built from these matrices, is described. Two-dimensional information is represented by the set of curve points. It is shown how to create the orthogonal and discrete OHR and how to use it in a process of data foreseeing and extrapolation. MHR method is interpolating and extrapolating the curve point by point without using any formula or function.

[1] Brachman R. and Levesque H., Knowledge Representation and Reasoning, Morgan Kaufman, 2004. (19) (18) 9721.37 9882.30767.429158.34 Information Analysis and 2D Point Extrapolation using Method ... 241

[2] Citko W., Jakóbczak D., and Sieńko W., “On Hurwitz-Radon Matrices Based Signal Processing,” in Proceedings of Workshop Signal Processing at Poznan University of Technology, Poznan, pp. 19-24, 2005.

[3] Dahlquist G. and Bjoerck A., Numerical Methods, Prentice Hall, 1974.

[4] Eckmann B., “Topology, Algebra, Analysis- Relations and Missing Links,” Notices of the American Mathematical Society, vol. 46, no. 5, pp. 520-527, 1999.

[5] Fagin R., Halpern J., Moses Y., and Vardi M., Reasoning About Knowledge, MIT Press, 1995.

[6] Jakóbczak D., “2D and 3D Image Modeling Using Hurwitz-Radon Matrices,” Polish Journal of Environmental Studies, vol. 16, no. 16, pp. 104- 107, 2007.

[7] Jakóbczak D., “Shape Representation and Shape Coefficients via Method of Hurwitz-Radon Matrices,” in Proceedings of International Conference on Computer Vision and Graphics, Warsaw, pp. 411-419, 2010.

[8] Jakóbczak D., “Curve Interpolation Using Hurwitz-Radon Matrices,” Polish Journal of Environmental Studies, vol. 18, no. 3B, pp. 126- 130, 2009.

[9] Jakóbczak D., Applied Computer Science: Modelling of Production Processes, Lublin University of Technology Press, 2010.

[10] Jakóbczak D., Computer Graphics: Selected Issues, University of Szczecin Press, 2010.

[11] Jakóbczak D., Image Processing and Communications: Challenges 2, Springer-Verlag, Berlin Heidelberg, 2010.

[12] Jakóbczak, D., Knowledge-Based Intelligent System Advancements: Systemic and Cybernetic Approaches, IGI Global, 2011.

[13] Kozera R., Studia Informatica, Silesian University of Technology Press, 2004.

[14] Markman A., Knowledge Representation, Lawrence Erlbaum Associates, 1998.

[15] Ralston, A., A First Course in Numerical Analysis, McGraw-Hill Book Company, 1965.

[16] Sieńko W., Citko W., and Wilamowski B., “Hamiltonian Neural Nets as a Universal Signal Processor,” in Proceedings of 28th Annual Conference of the Industrial Electronics Society, Sevilla, pp. 3201-3204, 2002.

[17] Sieńko W., Citko W., and Jakóbczak D., “Learning and System Modeling Via Hamiltonian Neural Networks,” in Proceedings of International Conference on Artificial Intelligence and Soft Computing, Zakopane, pp. 266-271, 2004.

[18] Soussen C. and Mohammad-Djafari A., “Polygonal and Polyhedral Contour Reconstruction in Computed Tomography,” IEEE Transactions on Image Processing, vol. 13, no. 11, pp. 1507-1523, 2004.

[19] Sowa J., Knowledge Representation: Logical, Philosophical and Computational Foundations, Brooks/Cole, 2000.

[20] Straffin P., Game Theory and Strategy, American Mathematical Society, 1993.

[21] Tang K., “Geometric Optimization Algorithms in Manufacturing,” Computer-Aided Design and Applications, vol. 2, no. 6, pp. 747-757, 2005.

[22] Tarokh V., Jafarkhani H., and Calderbank R., “Space-Time Block Codes from Orthogonal Designs,” IEEE Transactions on Information Theory, vol. 45, no. 5, pp. 1456-1467, 1999.

[23] Vairavan T. and Vani K., “An Efficient Age Estimation System with Facial Makeover Images Based on Key Points Selection,” The International Arab Journal of Information Technology, vol. 14, no. 1, pp. 8-17, 2017.

[24] Watson J., Strategy-An Introduction to Game Theory, University of California, San Diego, 2002. Dariusz Jakóbczak was born in Koszalin, Poland, on December 30, 1965. He graduated in mathematics (numerical methods and programming) from the University of Gdansk, Poland in 1990. He received the Ph.D. degree in 2007 in computer science from the Polish-Japanese Institute of Information Technology, Warsaw, Poland. From 1991 to 1994 he was a civilian programmer in the High Military School in Koszalin. He was a teacher of mathematics and computer science in the Private Economic School in Koszalin from 1995 to 1999. Since March 1998 he has worked in the Department of Electronics and Computer Science, Koszalin University of Technology, Poland and since October 2007 he has been an Assistant Professor in the Chair of Computer Science and Management in this department. His research interests connect mathematics with computer science and include computer vision, artificial intelligence, shape representation, curve interpolation, contour reconstruction and geometric modeling, numerical methods, probabilistic methods, game theory, operational research and discrete mathematics.